[tex]\sqrt{3x-1}-\sqrt{3x+1}>-1\\
\sqrt{3x-1}+1>\sqrt{3x+1}\\
(\sqrt{3x-1}+1)^2>(\sqrt{3x+1})^2\\
(\sqrt{3x-1})^2+2\cdot \sqrt{3x-1} \cdot 1+1^2>3x+1\\
3x-1+2\cdot \sqrt{3x-1}+1>3x+1\\
2\cdot \sqrt{3x-1}>1\\
\sqrt{3x-1}>\frac{1}{2}\\
(\sqrt{3x-1})^2>(\frac{1}{2})^2[/tex]
[tex]3x-1>\frac{1}{4}\\
3x>\frac{1}{4}+1\\
3x>\frac{5}{4}\\
x>\frac{5}{4}:3\\
x>\frac{5}{4} \cdot \frac{1}{3}[/tex]
[tex]x> \frac{5}{12}=>x \in ( \frac{5}{12},+ \infty)
[/tex]
